Show that a product of unitary (orthogonal) matrices is unitary (orthogonal) as well.
This is one of my review problems, but I am having difficulty starting because my definition of a unitary operator is that it is an invertible isometry. So this tells us, for some matrix U, U* U = I. But I guess I am sort of lost as to where to go from there.
Are you able to use the fact that, for unitary matrices A and B, |Det(A)|=1, so |Det(AB)|=|Det(A)||Det(B)|=(1)(1)=1. So |Det(AB)|=1, which is a property of unitary matrices. Or is this not enough?